CN116155329A - User clustering and power distribution method of mMIMO-NOMA system based on meta-heuristic algorithm - Google Patents

User clustering and power distribution method of mMIMO-NOMA system based on meta-heuristic algorithm Download PDF

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CN116155329A
CN116155329A CN202310436619.6A CN202310436619A CN116155329A CN 116155329 A CN116155329 A CN 116155329A CN 202310436619 A CN202310436619 A CN 202310436619A CN 116155329 A CN116155329 A CN 116155329A
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cluster
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CN116155329B (en
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李旺旺
黄学军
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Nanjing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0452—Multi-user MIMO systems
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a user clustering and power distribution method of an mMIMO-NOMA system based on a meta-heuristic algorithm, which comprises the following steps: firstly, constructing a millimeter wave mMIMO-NOMA system and constructing a millimeter wave channel model; step two, clustering all users by adopting a user clustering algorithm based on cluster head selection to obtain a user clustering result; step three, mixed pre-coding is carried out aiming at the obtained cluster head channels, and user interference among clusters is eliminated; and fourthly, performing power distribution by using a meta-heuristic algorithm based on fusion PSO-SCSO, and improving the frequency spectrum efficiency and the energy efficiency of the system. The invention is suitable for the multi-user millimeter wave mMIMO-NOMA system, and can effectively improve the frequency spectrum efficiency and the energy efficiency of the system.

Description

User clustering and power distribution method of mMIMO-NOMA system based on meta-heuristic algorithm
Technical Field
The invention belongs to the technical field of millimeter wave communication, and particularly relates to a user clustering and power distribution method of an mMIMO-NOMA system based on a meta-heuristic algorithm.
Background
Currently, wireless communication systems are mainly based on an orthogonal multiple access method, in which spectrum efficiency is low and the number of user accesses is limited. Millimeter wave technology can provide richer spectrum resources; the large-scale multiple input multiple output (massive multiple input multiple output, mMIMO) technology can improve the frequency spectrum efficiency by utilizing space division multiplexing and can compensate the path loss of millimeter waves; the non-orthogonal multiple access (non-orthogonal multiple access, NOMA) technology realizes power domain multiplexing through a serial interference cancellation technology, so that a plurality of users share the same time-frequency resource, and the number of simultaneous connections of the system can be effectively improved. Therefore, millimeter wave MIMO and NOMA are combined, namely a millimeter wave mMIMO-NOMA system, the mixed multiple access of SDMA and NOMA is realized by utilizing an antenna array of MIMO in a clustering mode, the limit of the number of radio frequency chains on the number of user connections can be broken through, and the system is expected to provide data transmission with higher speed and lower power consumption for future wireless networks.
In an mMIMO-NOMA communication system, as the number of users increases, the interference among users can obviously influence the system performance, the interference among different clusters can be solved by a hybrid precoding technology, and the interference among users in the clusters needs to be solved by a reasonable user clustering and power distribution algorithm. In recent years, domestic and foreign scholars have made a great deal of researches on hybrid precoding, user clustering and power distribution, wherein more researches are concentrated on hybrid precoding, more scholars have researched user clustering and power distribution, and various schemes are provided, but the existing power distribution problem is mainly solved by a convex optimization method, the calculation complexity is high, and the traditional machine learning-based user clustering algorithm also needs more complex calculation; in recent years, scholars have proposed using a meta-heuristic algorithm to solve the problem of power allocation of a NOMA system, but in a mMIMO-NOMA system, the number of users increases, and the performance decreases due to defects existing in the traditional meta-heuristic algorithm, so that the design of an efficient user clustering and power allocation algorithm for the mMIMO-NOMA system has important significance.
Disclosure of Invention
The invention provides a user clustering and power distribution method of an mMIMO-NOMA system based on a meta-heuristic algorithm aiming at solving the complex problem of user clustering and power distribution in the mMIMO-NOMA system, and particularly comprises an improved user clustering algorithm based on cluster head selection and an improved meta-heuristic algorithm of fusion particle swarm algorithm (particle swarm optimization, PSO) and a sand cat algorithm (Sand Cat Swarm Optimization, SCSO) for a power distribution scheme, aiming at reducing the calculation complexity and improving the frequency spectrum efficiency and the energy efficiency of the system.
In order to achieve the above object, the present invention provides a method for user clustering and power allocation of an mimo-NOMA system based on a meta-heuristic algorithm, comprising the steps of:
firstly, constructing a millimeter wave mMIMO-NOMA system and constructing a millimeter wave channel model;
step two, clustering all users by adopting a user clustering algorithm based on cluster head selection to obtain a user clustering result;
step three, mixed pre-coding is carried out aiming at the obtained cluster head channels, and user interference among clusters is eliminated;
and step four, performing power distribution by using a meta-heuristic algorithm based on fusion PSO-SCSO.
As a further improvement of the present invention, in the first step, the millimeter wave mMIMO-NOMA system comprises a digital precoding module, an analog precoding module and G user clusters, and the first step is that
Figure SMS_1
The cluster contains user->
Figure SMS_2
And the user data flow flows into a digital precoding module after being overlapped according to grouping and power distribution, then flows into an analog precoding module and finally is sent to each user.
As a further improvement of the present invention, clusters
Figure SMS_3
Middle->
Figure SMS_4
The signals received by the individual users are:
Figure SMS_5
wherein,,
Figure SMS_10
representing cluster->
Figure SMS_15
Middle user->
Figure SMS_23
Is>
Figure SMS_8
Representing cluster->
Figure SMS_17
Middle user->
Figure SMS_11
Is a signal received by the base station;
Figure SMS_16
，
Figure SMS_20
，
Figure SMS_26
representing cluster->
Figure SMS_9
Middle user->
Figure SMS_13
Transmit power of>
Figure SMS_22
Representing cluster->
Figure SMS_30
Middle user->
Figure SMS_24
Transmit power of>
Figure SMS_28
Representing cluster->
Figure SMS_29
Middle user->
Figure SMS_34
Transmit power of>
Figure SMS_36
Representing cluster->
Figure SMS_41
Middle user->
Figure SMS_6
Is>
Figure SMS_12
Representing cluster->
Figure SMS_18
Middle user->
Figure SMS_21
Is>
Figure SMS_35
Is cluster->
Figure SMS_42
Middle user->
Figure SMS_27
Is a Gaussian noise vector of>
Figure SMS_33
；
Figure SMS_32
Is an analog precoding matrix, < >>
Figure SMS_38
Is the conjugate transpose operation of the matrix,/->
Figure SMS_39
Namely +.>
Figure SMS_43
Is a conjugate transpose of (2);
Figure SMS_19
Representing the +.>
Figure SMS_25
Column (S)/(S)>
Figure SMS_7
Representing the +.>
Figure SMS_14
Column (S)/(S)>
Figure SMS_31
Representing cluster->
Figure SMS_37
Middle user->
Figure SMS_40
Adopts a millimeter wave channel model of a uniform planar array.
As a further improvement of the invention, a user clustering algorithm based on cluster head selection is adopted in the second step to carry out self-adaptive clustering on all users, and the method specifically comprises the following steps:
clustering users according to channel correlation by utilizing the directivity characteristic of millimeter waves, wherein the users in the same cluster use the same analog precoding, namely, the beam gain is obtained from the same beam; the correlation of user channels in the same cluster is high, and the correlation of user channels in different clusters is low; the cluster head user is a strong user in each cluster; the specific algorithm process is as follows:
step1. initializing: initializing user channel gain vectors
Figure SMS_46
Wherein->
Figure SMS_49
；
Figure SMS_52
Is->
Figure SMS_45
Channel vector for individual user->
Figure SMS_47
，
Figure SMS_50
Representing the total number of users; cluster head set->
Figure SMS_53
Initially empty; initialization threshold +.>
Figure SMS_44
The method comprises the steps of carrying out a first treatment on the surface of the Setting the maximum number of users in each cluster +.>
Figure SMS_48
；
Figure SMS_51
；
Step2, selecting the channel corresponding to the largest element in the current channel gain vector
Figure SMS_54
As the current cluster head and removing it from the channel set and channel gain vector;
step3, calculating all remaining user channels in the channel set
Figure SMS_55
Correlation with current cluster head
Figure SMS_56
If and only if the number of users in the cluster does not exceed +.>
Figure SMS_57
And->
Figure SMS_58
When in use, will->
Figure SMS_59
The corresponding user is classified as the corresponding user of the current cluster head>
Figure SMS_60
Clusters and removing them from the remaining set of user channels;
Step4.
Figure SMS_61
；
step5 repeating Step3 and Step4 until all users have completed clustering, and setting all users to be classified together
Figure SMS_62
Cluster, th->
Figure SMS_63
The cluster contains user->
Figure SMS_64
If yes, all users are used +.>
Figure SMS_65
And (3) representing.
As a further improvement of the present invention, hybrid precoding is used in step three, including analog precoding and digital precoding, wherein the analog precoding is implemented using a phase shifter, only adjusting the phase of the signal; the digital precoding is implemented by a radio frequency chain to adjust both phase and amplitude.
As a further improvement of the invention, in the fourth step, aiming at maximizing the spectral efficiency and the energy efficiency of the system, a meta-heuristic algorithm fused with PSO-SCSO is adopted to solve the user power distribution, and by improving the particle movement mode and fusing with the SCSO algorithm, more accurate results can be obtained after fewer times of iteration.
As a further improvement of the present invention, the meta-heuristic algorithm fusing PSO-SCSO includes:
the PSO-SCSO algorithm is fused, the particle swarm algorithm PSO and the salsa optimization algorithm SCSO are combined, and the development capacity and the global searching capacity of the PSO are improved by utilizing the high-dimensional searching capacity of the SCSO; the fusion PSO-SCSO algorithm updates the particle position in an improved way, and comprises the following algorithm steps:
step1, initializing the size of particle populations, initializing all parameters, and randomly initializing the particle populations;
step2, calculating the fitness value of all particles, and if the fitness value is better than the fitness value of the global optimal position, updating the global optimal position;
step3, updating the positions of all particles by using the following formula;
Figure SMS_66
wherein,,
Figure SMS_81
indicate->
Figure SMS_71
The individual particles are at->
Figure SMS_76
Position vector in the iterative process of times;
Figure SMS_80
Indicate->
Figure SMS_85
The individual particles are at->
Figure SMS_84
Position vector in the iterative process of times;
Figure SMS_86
Is a vector introduced;
Figure SMS_72
、
Figure SMS_78
、
Figure SMS_67
Are random numbers between 0 and 1 subject to uniform distribution, ">
Figure SMS_73
Is 0 to->
Figure SMS_70
Obeying betweenA uniformly distributed random value;
Figure SMS_77
、
Figure SMS_79
Are all intermediate variables of the formula, and respectively represent main position updating modes of the particles in the early stage and the later stage of movement;
Figure SMS_83
Is a global optimal position vector in each iteration process;
Figure SMS_69
Is a scalar with an initial value of +.>
Figure SMS_74
Gradually reducing in the iterative process;
Figure SMS_75
Is a control coefficient;
Figure SMS_82
And->
Figure SMS_68
Are all acceleration factors;
step4, repeating Step2 and Step3 until the algorithm converges;
step5. Output algorithm updates the location information.
The beneficial effects of the invention are as follows: the invention is suitable for millimeter wave mMIMO-NOMA multi-user systems, adopts a user clustering algorithm based on cluster head selection to cluster users, aims at maximizing the weighted sum of spectrum efficiency and energy efficiency, and adopts an improved meta-heuristic algorithm to carry out power distribution; compared with the traditional meta-heuristic algorithm, the meta-heuristic algorithm shows more accurate search results and faster search speed; which is used for system power allocation, can enable the system to achieve higher spectral and energy efficiency and reduce computational complexity.
Drawings
Fig. 1 is a flow chart of a user clustering and power allocation method for a meta-heuristic based mimo-NOMA system in an embodiment of the present invention.
Fig. 2 is a diagram of a millimeter wave mimo-NOMA system model in an embodiment of the present invention.
Figure 3 is an algorithm flow diagram of a meta-heuristic algorithm incorporating the PSO-SCSO algorithm in an embodiment of the invention.
FIG. 4 is a graph of an algorithm convergence analysis in an embodiment of the invention.
Fig. 5 is a schematic diagram showing a comparison between the spectral efficiency and the signal-to-noise ratio of a system of the power allocation algorithm according to an embodiment of the present invention.
Fig. 6 is a schematic diagram showing a comparison between the system energy efficiency and the signal to noise ratio of the power distribution algorithm according to the embodiment of the present invention.
Fig. 7 is a schematic diagram showing a comparison between the spectral efficiency and the signal-to-noise ratio of a system of a user clustering algorithm according to an embodiment of the present invention.
FIG. 8 is a diagram illustrating a comparison of system energy efficiency and signal-to-noise ratio for a user clustering algorithm according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the present invention provides a user clustering and power allocation method for an mimo-NOMA system based on a meta-heuristic algorithm, which mainly includes the following steps:
firstly, constructing a millimeter wave mMIMO-NOMA system and constructing a millimeter wave channel model;
step two, clustering all users by adopting a user clustering algorithm based on cluster head selection to obtain a user clustering result;
step three, mixed pre-coding is carried out aiming at the obtained cluster head channels, and user interference among clusters is eliminated;
and step four, performing power distribution by using a meta-heuristic algorithm based on fusion PSO-SCSO.
The following describes the steps one to four in detail with reference to the accompanying drawings.
In the first step, the first step is to perform,the millimeter wave mMIMO-NOMA system comprises a digital precoding module, an analog precoding module and G user clusters, and is characterized in that
Figure SMS_87
The cluster contains user->
Figure SMS_88
And the user data flow flows into a digital precoding module after being overlapped according to grouping and power distribution, then flows into an analog precoding module and finally is sent to each user.
That is, the first step is specifically: constructing a multi-user millimeter wave mMIMO-NOMA system model shown in figure 2, wherein a BS end is provided with
Figure SMS_89
Root transmitting antenna and->
Figure SMS_90
RF chains, simultaneously serving->
Figure SMS_91
A random distribution of single antenna users, +.>
Figure SMS_92
Figure SMS_93
Figure SMS_94
。
In order to obtain multiplexing gain sufficiently, the number of RF chains is set equal to the number of beams
Figure SMS_95
。
By NOMA technique, users are classified into
Figure SMS_96
Cluster, th->
Figure SMS_97
Total->
Figure SMS_98
The same beam is shared by the individual users.
Order the
Figure SMS_99
、
Figure SMS_100
Respectively representing an analog precoding matrix and a digital precoding matrix in hybrid precoding, then the cluster +.>
Figure SMS_101
Middle->
Figure SMS_102
The signals received by the individual users are expressed as: />
Figure SMS_103
（1）
Wherein,,
Figure SMS_132
representing cluster->
Figure SMS_137
Middle user->
Figure SMS_139
Is>
Figure SMS_108
Representing cluster->
Figure SMS_114
Middle user->
Figure SMS_120
Is a signal received by the base station;
Figure SMS_127
，
Figure SMS_128
，
Figure SMS_133
representing cluster->
Figure SMS_135
Middle user->
Figure SMS_140
Transmit power of>
Figure SMS_130
Representing cluster->
Figure SMS_134
Middle user->
Figure SMS_138
Transmit power of>
Figure SMS_142
Representing cluster->
Figure SMS_111
Middle user->
Figure SMS_119
Transmit power of>
Figure SMS_123
Representing cluster->
Figure SMS_129
Middle user->
Figure SMS_104
Is>
Figure SMS_110
Representing cluster->
Figure SMS_116
Middle user->
Figure SMS_122
Is>
Figure SMS_109
And->
Figure SMS_115
The range of values of ++as described in the cumulative notation>
Figure SMS_117
Is cluster->
Figure SMS_126
Middle user->
Figure SMS_131
Is a Gaussian noise vector of>
Figure SMS_136
；
Figure SMS_141
Is an analog precoding matrix, < >>
Figure SMS_143
Is the conjugate transpose operation of the matrix,/->
Figure SMS_106
Namely
Figure SMS_112
Is a conjugate transpose of (2);
Figure SMS_121
Representing the +.>
Figure SMS_125
Column (S)/(S)>
Figure SMS_107
Representing the +.>
Figure SMS_113
The number of columns in a row,
Figure SMS_118
representing cluster->
Figure SMS_124
Middle user->
Figure SMS_105
Adopts a millimeter wave channel model of a uniform plane array, and the signal-to-interference-and-noise ratio corresponding to a user is as follows:
Figure SMS_144
（2）
wherein:
Figure SMS_145
（3）
wherein,,
Figure SMS_146
representing the +.>
Figure SMS_147
Columns.
In the second step, a user clustering algorithm based on cluster head selection is adopted to perform self-adaptive clustering on all users, and a user clustering result is obtained, and the specific method is as follows:
clustering users according to channel correlation by utilizing the directivity characteristic of millimeter waves, wherein the users in the same cluster use the same analog precoding, namely, the beam gain is obtained from the same beam; the correlation of user channels in the same cluster is high, and the correlation of user channels in different clusters is low; the cluster head user is a strong user in each cluster; the specific algorithm process is as follows:
step1. initializing: initializing user channel gain vectors
Figure SMS_149
Wherein->
Figure SMS_153
；
Figure SMS_156
Is->
Figure SMS_150
Channel vector for individual user->
Figure SMS_152
，
Figure SMS_154
Representing the total number of users; cluster head set->
Figure SMS_157
Initially empty; initialization threshold +.>
Figure SMS_148
The method comprises the steps of carrying out a first treatment on the surface of the Setting the maximum number of users in each cluster +.>
Figure SMS_151
；
Figure SMS_155
；
Step2, selecting the channel corresponding to the largest element in the current channel gain vector
Figure SMS_158
As the current cluster head and removing it from the channel set and channel gain vector;
step3, calculating all remaining user channels in the channel set
Figure SMS_159
Correlation with current cluster head
Figure SMS_160
If and only if the number of users in the cluster does not exceed +.>
Figure SMS_161
And->
Figure SMS_162
When in use, will->
Figure SMS_163
The corresponding user is classified as the corresponding user of the current cluster head>
Figure SMS_164
Clusters and removing them from the remaining set of user channels; />
Step4.
Figure SMS_165
；
Step5 repeating Step3 and Step4 until all users have completed clustering, and setting all users to be classified together
Figure SMS_166
Cluster, th->
Figure SMS_167
The cluster contains user->
Figure SMS_168
If yes, all users are used +.>
Figure SMS_169
And (3) representing.
Step three, hybrid precoding is used, which comprises analog precoding and digital precoding, wherein the analog precoding is realized by using a phase shifter, and only the phase of a signal is adjusted; the digital precoding is implemented by a radio frequency chain to adjust both phase and amplitude.
The third step is as follows: hybrid precoding is performed on the obtained cluster head channels, so that user interference among clusters is eliminated, and a precoding matrix is simulated
Figure SMS_170
Only the phase of the signal can be adjusted, so analog precoding is designed considering the phase using the conjugate transpose of the channel matrix, while taking into account the accuracy problem of the phase shifter, assuming +.>
Figure SMS_171
Bit-accurate phase shifters, the analog precoding matrix can be expressed as:
Figure SMS_172
（4）
wherein,,
Figure SMS_174
is the cluster head channel of the G user clusters, < >>
Figure SMS_178
Representation->
Figure SMS_181
Is>
Figure SMS_175
Line->
Figure SMS_177
Element(s)>
Figure SMS_180
Representation->
Figure SMS_183
Is>
Figure SMS_173
Line->
Figure SMS_176
Element(s)>
Figure SMS_179
Is an intermediate variable,/->
Figure SMS_182
Representing calculating the phase angle of the complex number. After obtaining the analog precoding, obtaining the equivalent channels of all cluster head users as
Figure SMS_184
（5）
The digital precoding matrix is:
Figure SMS_185
（6）
in the fourth step, aiming at maximizing the spectral efficiency and the energy efficiency of the system, a meta-heuristic algorithm fused with PSO-SCSO is adopted to solve the user power distribution, and a particle motion mode is improved, and the SCSO algorithm is fused, so that a more accurate result can be obtained after fewer iterations.
The meta-heuristic algorithm for fusing PSO-SCSO comprises the following steps:
the PSO-SCSO algorithm is fused, the particle swarm algorithm PSO and the salsa optimization algorithm SCSO are combined, and the development capacity and the global searching capacity of the PSO are improved by utilizing the high-dimensional searching capacity of the SCSO; the fusion PSO-SCSO algorithm updates the particle position in an improved way, and comprises the following algorithm steps:
step1, initializing the size of particle populations, initializing all parameters, and randomly initializing the particle populations;
step2, calculating the fitness value of all particles, and if the fitness value is better than the fitness value of the global optimal position, updating the global optimal position;
step3, updating the positions of all particles by using the following formula;
Figure SMS_186
wherein,,
Figure SMS_194
indicate->
Figure SMS_188
The individual particles are at->
Figure SMS_198
Position vector in the iterative process of times;
Figure SMS_189
Indicate->
Figure SMS_196
The individual particles are at->
Figure SMS_200
Multiple iterationsA position vector in the process;
Figure SMS_204
For an introduced vector, it is defined in equation (17);
Figure SMS_199
、
Figure SMS_203
、
Figure SMS_187
Are random numbers between 0 and 1 subject to uniform distribution, ">
Figure SMS_193
Is 0 to->
Figure SMS_201
Random values subject to uniform distribution;
Figure SMS_206
、
Figure SMS_202
Are all intermediate variables of the formula, and respectively represent main position updating modes of the particles in the early stage and the later stage of movement;
Figure SMS_205
Is a global optimal position vector in each iteration process;
Figure SMS_191
Is a scalar with an initial value of +.>
Figure SMS_195
Gradually reducing in the iterative process;
Figure SMS_192
Is a control coefficient;
Figure SMS_197
And->
Figure SMS_190
Are acceleration factors, which are defined in equation (19);
step4, repeating Step2 and Step3 until the algorithm converges;
step5. Output algorithm updates the location information.
Specifically, in the fourth step, a meta-heuristic algorithm based on fusion PSO-SCSO is used for power distribution so as to improve the frequency spectrum efficiency and the energy efficiency of the system.
Firstly, determining an optimization target, after completing mixed precoding, firstly sequencing and renumbering users in a cluster according to channel gains, wherein the sequencing result satisfies the following conditions:
Figure SMS_207
the information transmission rate of the mth user in the g cluster is expressed as follows:
Figure SMS_208
（7）
the spectral efficiency of the system is expressed as;
Figure SMS_209
（8）
the energy efficiency of the system is defined as the number of bits per joule of energy transmitted, expressed as follows:
Figure SMS_210
（9）
wherein the method comprises the steps of
Figure SMS_211
、
Figure SMS_212
、
Figure SMS_213
Respectively represents the power of each radio frequency chain, the power of each phase shifter and the power of the base band, +.>
Figure SMS_214
Indicating the number of phase shifters. Since the spectrum efficiency and the energy efficiency are key indexes of mobile communication, the invention considers the maximization of the weighted sum of the spectrum efficiency and the energy efficiency as an optimization target to construct the following optimization problems: />
Figure SMS_215
（10）
Wherein,,
Figure SMS_216
indicating that the transmission power of each user should be a positive number,/->
Figure SMS_217
Indicating that the total transmit power of all users is less than the maximum transmit power of the base station +.>
Figure SMS_218
，
Figure SMS_219
Is the information transmission rate of the mth user in the g cluster, see formula (7), for->
Figure SMS_220
Ensuring that the information transmission rate of each user meets the minimum rate requirement +.>
Figure SMS_221
。
For easy solution, according to the characteristics of the algorithm, neglect
Figure SMS_222
Constraint, converting the constraint maximizing optimization problem into an unconstrained minimizing optimization problem by using a penalty function:
Figure SMS_223
（11）
wherein,,
Figure SMS_225
representing the spectral efficiency of the system, see equation (8);
Figure SMS_228
Representing the energy efficiency of the system, see equation (9); ρ is a penalty factor; the system is divided into G clusters, th->
Figure SMS_230
There is +.>
Figure SMS_226
Individual user (s)/(S)>
Figure SMS_227
Is the transmission power of the mth user in the g-th cluster, and>
Figure SMS_229
is the total transmit power constraint of the system;
Figure SMS_231
Is the spectral efficiency of the mth user in the g cluster,/->
Figure SMS_224
Is the lowest spectral efficiency that meets the individual user requirements.
Aiming at the minimization and optimization problem (11), the traditional optimization algorithm based on classical mathematical theory has a complex calculation process; and the meta-heuristic algorithm obtains a global optimal value through simple calculation by global random search, improves the system performance in order to fully exert the global searching capability of the algorithm, improves the PSO algorithm and fuses the SCSO algorithm.
PSO algorithm:
the PSO algorithm starts from a random initial value, and finally determines a global optimal solution by tracking a local optimal solution in each iteration process. The method is characterized by simple structure and high calculation speed, and is very suitable for solving the multi-objective optimization problem. In the standard PSO algorithm, let
Figure SMS_232
And->
Figure SMS_233
Respectively represent +.>
Figure SMS_234
The individual particles are at->
Figure SMS_235
Position vector and velocity vector in the next iteration process, then +.>
Figure SMS_236
Individual particles from->
Figure SMS_237
Iteration number to->
Figure SMS_238
The next state update formula is as follows:
Figure SMS_239
（12）
wherein,,
Figure SMS_241
、
Figure SMS_244
is a random number between 0 and 1 subject to uniform distribution, ">
Figure SMS_247
Indicate->
Figure SMS_242
The individual particles are at->
Figure SMS_243
Optimal position of the iteration->
Figure SMS_246
Representing a global optimum position->
Figure SMS_248
As inertial weight, trust in previous motion state of particles is represented;
Figure SMS_240
，
Figure SMS_245
the acceleration factors represent the trust of the experience of the particle and the global shared information. Although the PSO algorithm is simple to implement and has high convergence rate, the PSO algorithm also has the defect of being easy to fall into local optimum because the particle motion direction of the PSO algorithm is relatively fixed, so that the PSO algorithm is easy to converge in premature.
SCSO algorithm:
the SCSO algorithm is an optimization algorithm for simulating the survival behavior of the sand cat newly proposed in 2022, has the characteristics of high convergence speed and accurate result, and is better in high-dimensional and multi-objective optimization. Order the
Figure SMS_249
Representing from->
Figure SMS_250
Iterative update to +.>
Figure SMS_251
The new position of the population obtained by the iteration is shown in the following formula for updating the particles of the SCSO algorithm.
Figure SMS_252
（13）
Wherein,,
Figure SMS_254
is->
Figure SMS_256
Sub-globally optimal solution,/->
Figure SMS_259
Is a populationMiddle Member->
Figure SMS_255
The position of the moment->
Figure SMS_257
Representation->
Figure SMS_260
Local optimal position of each member at moment->
Figure SMS_261
Is a random angle for controlling each member of the population to move in different directions in the search space,/or->
Figure SMS_253
And->
Figure SMS_258
Is a random number between 0 and 1. Other parameters are obtained by the formulas (14 to 16).
Figure SMS_262
(14)
Figure SMS_263
(15)
Figure SMS_264
(16)
Wherein,,
Figure SMS_265
、
Figure SMS_266
is a random number between 0 and 1, ">
Figure SMS_267
Representing the sensitivity range of each sand cat, and generally setting to be 2;
Figure SMS_268
、
Figure SMS_269
Respectively representing the current iteration number and the maximum iteration number, < ->
Figure SMS_270
Is an intermediate variable,/->
Figure SMS_271
Is a distance parameter for controlling the behavior of the sand cat.
Fusion PSO-SCSO algorithm
In light of the above description, the PSO algorithm is first improved in order to accelerate the convergence speed of the algorithm and improve the global search capability of the algorithm, and the location update formula is improved as follows:
Figure SMS_272
(17)
wherein,,
Figure SMS_277
indicate->
Figure SMS_274
The individual particles are at->
Figure SMS_279
Position vector of the iterative procedure,/->
Figure SMS_276
Indicate->
Figure SMS_281
The individual particles are at->
Figure SMS_286
Position vector in the course of a second iteration, +.>
Figure SMS_290
Representing the upper boundary of the position coordinates of all particles, +.>
Figure SMS_285
Representing the lower boundary of the position coordinates of all particles, +.>
Figure SMS_289
Representing a globally optimal solution vector,>
Figure SMS_273
、
Figure SMS_280
、
Figure SMS_278
are random numbers between 0 and 1, ">
Figure SMS_282
The elements are 0 to->
Figure SMS_283
Random value between->
Figure SMS_288
Represents the step size of the exercise>
Figure SMS_275
Control convergence rate, ++>
Figure SMS_284
The initial value is->
Figure SMS_287
。
In equation (17), the first term replaces the inertia and local optimum factors in the original equation,
Figure SMS_291
is a vector pointing to a globally optimal solution, a sine function is used as a coefficient, and the result of the vector is to drive particles to approach or depart from the globally optimal position, wherein the probability ratio of the two is 2:1, such a design accelerates the convergence speed of the algorithm; the second term is that cosine disturbance is added to the current position of the particles, so that the particles start from the current position and followThe machine moves in a range near the optimal position, so that the algorithm has better searching capability; in the third term, the acceleration factor in the original formula +.>
Figure SMS_292
The method is replaced by a sine expression, the value of the sine expression is reduced along with the increase of the iteration times, so that the particles are rapidly close to the optimal solution at the initial stage of the iteration, and slowly converged near the global optimal point at the later stage, thereby avoiding the oscillation of the particles near the optimal point and improving the convergence.
Referring again to the attack behavior in the SCSO algorithm, the third term in equation (17) is modified, and the variable coefficients are introduced, and the equation after the second modification is as follows:
Figure SMS_293
(18)
wherein,,
Figure SMS_306
indicate->
Figure SMS_297
The individual particles are at->
Figure SMS_300
Position vector in the iterative process of times;
Figure SMS_309
Indicate->
Figure SMS_313
The individual particles are at->
Figure SMS_310
Position vector in the iterative process of times;
Figure SMS_314
For a vector to be introduced, it is defined as in equation (17);
Figure SMS_307
、
Figure SMS_311
、
Figure SMS_294
are random numbers between 0 and 1 subject to uniform distribution, ">
Figure SMS_305
Is 0 to->
Figure SMS_298
Random values subject to uniform distribution;
Figure SMS_301
、
Figure SMS_299
Are all intermediate variables of the formula, and respectively represent main position updating modes of the particles in the early stage and the later stage of movement;
Figure SMS_304
Is a global optimal position vector in each iteration process;
Figure SMS_296
Is a scalar with an initial value of +.>
Figure SMS_302
Gradually reducing in the iterative process;
Figure SMS_308
Is a control coefficient;
Figure SMS_312
And->
Figure SMS_295
All are acceleration factors, the value and +.>
Figure SMS_303
The related steps are as follows:
Figure SMS_315
(19)
in the formulae (18) to (19),
Figure SMS_318
、
Figure SMS_321
、
Figure SMS_323
the value of (2) is adjusted according to the actual problem>
Figure SMS_317
The calculation of (1) is the same as in the sand cat algorithm. The improved algorithm takes the distance from the global optimum point as a parameter, if +.>
Figure SMS_320
，
Figure SMS_322
，
Figure SMS_324
Plays a main role, and promotes particles to approach to the optimal point; otherwise->
Figure SMS_316
,
Figure SMS_319
Plays a main role in promoting the searching of particles in a global scope.
The calculation flow of the fusion PSO-SCSO algorithm is shown in figure 3.
The transmitting power of all users is used as the position vector of particles in the algorithm, the algorithm converges after limited iterations, and the output result is the power distribution scheme of the users, so that the frequency spectrum efficiency and the energy efficiency of the system can be maximized.
Under the steps of the embodiment, the beneficial effects of the invention are illustrated by performing simulation experiments on the MATLAB platform.
The table below shows the simulation parameter settings,the system parameters in the table are removed, and the fusion PSO-SCSO algorithm parameters are as follows:
Figure SMS_326
，
Figure SMS_328
，
Figure SMS_332
，
Figure SMS_327
the method comprises the steps of carrying out a first treatment on the surface of the Penalty factor->
Figure SMS_330
，
Figure SMS_331
. Threshold +.>
Figure SMS_333
In a random selection +.>
Figure SMS_325
Individual user, let->
Figure SMS_329
Is 1.25 times the average value of the channel correlation between any two of the users, wherein 1.25 is the empirical value of multiple experiments. />
Figure SMS_334
Fig. 4 is a convergence simulation diagram of different meta-heuristic algorithms, comparing the proposed algorithm with the classical meta-heuristic algorithm, including PSO algorithm, wolf optimization (Grey Wolf Optimizer, GWO) algorithm, whale optimization (whale optimization algorithm, WOA) algorithm, and it can be seen from the diagram that the proposed algorithm achieves convergence within about 10 times, the convergence speed is the fastest and the fitness value is the lowest, and the convergence of the proposed algorithm is verified.
Fig. 5 and fig. 6 are respectively the relations of energy efficiency and spectral efficiency of different algorithms with signal to noise ratio, and it can be seen from fig. 5 that the spectral efficiency of all-digital precoding is the highest, representing the theoretical upper limit, but the cost is high, and it is difficult to apply to practice, so that only reference is made. In the NOMA power allocation scheme, as the signal-to-noise ratio increases, the proposed algorithm is closest to all-digital precoding, and is superior to other schemes. Fig. 6 shows the energy efficiency versus signal-to-noise ratio, and it can be seen from fig. 6 that although the spectral efficiency of all-digital precoding is highest, it is lowest because it requires a large number of radio frequency chains to implement; the NOMA system uses less radio frequency chains and utilizes power domain multiplexing, so that the energy efficiency is greatly improved; and the energy efficiency of the proposed algorithm is better than other algorithms because the proposed algorithm can achieve higher spectral efficiency with the same power consumption.
Fig. 7 and 8 compare the proposed user clustering algorithm with a K-means clustering algorithm, the number of clusters of which is set to a fixed value of 6. As can be seen from fig. 7, as the signal-to-noise ratio increases, the spectral efficiency of the proposed algorithm is significantly better than other algorithms, because the proposed algorithm of the present invention divides the user channels with higher correlation into a cluster, otherwise, they are used as a cluster alone; and the K-means algorithm forcedly divides all users into fixed clusters, so that the situation that the correlation of users in the clusters is low exists, the transmission rate of part of users is low, and the interference among the users in the clusters is not easy to eliminate. While the energy efficiency of the different clustering algorithms is shown in fig. 8, although the actual number of clusters of the proposed algorithm would be higher than the other algorithms, meaning that more RF chains and energy consumption are required, it can be seen from the figure that the energy efficiency is actually slightly higher than the K-means algorithm, so that such a scheme is reasonable.
In summary, the invention is suitable for millimeter wave mMIMO-NOMA multi-user systems, adopts a user clustering algorithm based on cluster head selection to cluster users, aims at maximizing the weighted sum of spectrum efficiency and energy efficiency, and adopts an improved meta-heuristic algorithm to perform power distribution; compared with the traditional meta-heuristic algorithm, the meta-heuristic algorithm shows more accurate search results and faster search speed; which is used for system power allocation, can enable the system to achieve higher spectral and energy efficiency and reduce computational complexity.
The above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the technical solution of the present invention.

Claims (7)

1. The user clustering and power distribution method of the mMIMO-NOMA system based on the meta-heuristic algorithm is characterized by comprising the following steps:
firstly, constructing a millimeter wave mMIMO-NOMA system and constructing a millimeter wave channel model;
step two, clustering all users by adopting a user clustering algorithm based on cluster head selection to obtain a user clustering result;
step three, mixed pre-coding is carried out aiming at the obtained cluster head channels, and user interference among clusters is eliminated;
and step four, performing power distribution by using a meta-heuristic algorithm based on fusion PSO-SCSO.
2. The meta-heuristic based user clustering and power allocation method of a mimo-NOMA system of claim 1, wherein: in the first step, the millimeter wave mimo-NOMA system includes a digital precoding module, an analog precoding module, and G user clusters, the first step
Figure QLYQS_1
The cluster contains user->
Figure QLYQS_2
And the user data flow flows into a digital precoding module after being overlapped according to grouping and power distribution, then flows into an analog precoding module and finally is sent to each user.
3. The meta-heuristic based user clustering and power allocation method of a mimo-NOMA system of claim 2, whereinIn that, the cluster
Figure QLYQS_3
Middle->
Figure QLYQS_4
The signals received by the individual users are:
Figure QLYQS_9
wherein (1)>
Figure QLYQS_13
Representing cluster->
Figure QLYQS_19
Middle user->
Figure QLYQS_6
Is>
Figure QLYQS_12
Representing cluster->
Figure QLYQS_8
Middle user->
Figure QLYQS_15
Is a signal received by the base station;
Figure QLYQS_22
，
Figure QLYQS_28
，
Figure QLYQS_10
Representing cluster->
Figure QLYQS_16
Middle user->
Figure QLYQS_18
Transmit power of>
Figure QLYQS_23
Representing cluster->
Figure QLYQS_24
Middle user->
Figure QLYQS_31
Transmit power of>
Figure QLYQS_30
Representing cluster->
Figure QLYQS_38
Middle user->
Figure QLYQS_34
Transmit power of>
Figure QLYQS_40
Representing cluster->
Figure QLYQS_5
Middle user->
Figure QLYQS_11
Is>
Figure QLYQS_20
Representing cluster->
Figure QLYQS_26
Middle user->
Figure QLYQS_33
Is>
Figure QLYQS_39
Is cluster->
Figure QLYQS_21
Middle user->
Figure QLYQS_27
Is a Gaussian noise vector of>
Figure QLYQS_29
；
Figure QLYQS_35
Is an analog pre-coding matrix that is used to determine,
Figure QLYQS_36
is the conjugate transpose operation of the matrix,/->
Figure QLYQS_42
Namely +.>
Figure QLYQS_17
Is a conjugate transpose of (2);
Figure QLYQS_25
Representing the +.>
Figure QLYQS_7
Column (S)/(S)>
Figure QLYQS_14
Representing the +.>
Figure QLYQS_32
Column (S)/(S)>
Figure QLYQS_37
Representing cluster->
Figure QLYQS_41
Middle user->
Figure QLYQS_43
Adopts a uniform planeMillimeter wave channel model of the array.
4. The method for user clustering and power distribution of a mimo-NOMA system based on a meta-heuristic algorithm according to claim 1, wherein in the second step, a user clustering algorithm based on cluster head selection is adopted to perform adaptive clustering on all users, and specifically comprises:
clustering users according to channel correlation by utilizing the directivity characteristic of millimeter waves, wherein the users in the same cluster use the same analog precoding, namely, the beam gain is obtained from the same beam; the correlation of user channels in the same cluster is high, and the correlation of user channels in different clusters is low; the cluster head user is a strong user in each cluster; the specific algorithm process is as follows: step1. initializing: initializing user channel gain vectors
Figure QLYQS_45
Wherein->
Figure QLYQS_47
，
Figure QLYQS_50
Is->
Figure QLYQS_46
The channel vector of the individual user(s),
Figure QLYQS_49
，
Figure QLYQS_52
representing the total number of users; cluster head set->
Figure QLYQS_53
Initially empty; initialization threshold +.>
Figure QLYQS_44
The method comprises the steps of carrying out a first treatment on the surface of the Setting the maximum number of users in each cluster +.>
Figure QLYQS_48
；
Figure QLYQS_51
The method comprises the steps of carrying out a first treatment on the surface of the Step2, selecting the channel corresponding to the largest element in the current channel gain vector>
Figure QLYQS_54
As the current cluster head and removing it from the channel set and channel gain vector; />
Step3, calculating all remaining user channels in the channel set
Figure QLYQS_55
Correlation with current cluster head
Figure QLYQS_56
If and only if the number of users in the cluster does not exceed +.>
Figure QLYQS_57
And->
Figure QLYQS_58
When in use, will->
Figure QLYQS_59
The corresponding user is classified as the corresponding user of the current cluster head>
Figure QLYQS_60
Clusters and removing them from the remaining set of user channels; step4.
Figure QLYQS_61
；
Step5 repeating Step3 and Step4 until all users have completed clustering, and setting all users to be classified together
Figure QLYQS_62
Cluster, th->
Figure QLYQS_63
The cluster contains user->
Figure QLYQS_64
If yes, all users are used +.>
Figure QLYQS_65
And (3) representing.
5. The meta-heuristic based user clustering and power allocation method of a mimo-NOMA system of claim 1, wherein: step three, hybrid precoding is used, which comprises analog precoding and digital precoding, wherein the analog precoding is realized by using a phase shifter, and only the phase of a signal is adjusted; the digital precoding is implemented by a radio frequency chain to adjust both phase and amplitude.
6. The meta-heuristic based user clustering and power allocation method of a mimo-NOMA system of claim 1, wherein: in the fourth step, aiming at maximizing the spectral efficiency and the energy efficiency of the system, a meta-heuristic algorithm fused with PSO-SCSO is adopted to solve the user power distribution, and a particle motion mode is improved, and the SCSO algorithm is fused, so that a more accurate result can be obtained after fewer iterations.
7. The meta-heuristic method for user clustering and power allocation of a mimo-NOMA system based on the meta-heuristic algorithm of claim 6 wherein the meta-heuristic algorithm fusing PSO-SCSO comprises:
the PSO-SCSO algorithm is fused, the particle swarm algorithm PSO and the salsa optimization algorithm SCSO are combined, and the development capacity and the global searching capacity of the PSO are improved by utilizing the high-dimensional searching capacity of the SCSO; the fusion PSO-SCSO algorithm updates the particle position in an improved way, and comprises the following algorithm steps: step1, initializing the size of particle populations, initializing all parameters, and randomly initializing the particle populations;
step2, calculating the fitness value of all particles, and if the fitness value is better than the fitness value of the global optimal position, updating the global optimal position;
step3, updating the positions of all particles by using the following formula;
Figure QLYQS_80
wherein (1)>
Figure QLYQS_68
Indicate->
Figure QLYQS_74
The individual particles are at->
Figure QLYQS_71
Position vector in the iterative process of times;
Figure QLYQS_76
Indicate->
Figure QLYQS_81
The individual particles are at->
Figure QLYQS_85
Position vector in the iterative process of times;
Figure QLYQS_70
Is a vector introduced;
Figure QLYQS_77
、
Figure QLYQS_66
、
Figure QLYQS_75
Are random numbers between 0 and 1 subject to uniform distribution, ">
Figure QLYQS_69
From 0 to 0
Figure QLYQS_73
Random values subject to uniform distribution;
Figure QLYQS_79
、
Figure QLYQS_84
Are all intermediate variables of the formula, and respectively represent main position updating modes of the particles in the early stage and the later stage of movement;
Figure QLYQS_78
Is a global optimal position vector in each iteration process;
Figure QLYQS_83
Is a scalar with an initial value of +.>
Figure QLYQS_82
Gradually reducing in the iterative process;
Figure QLYQS_86
Is a control coefficient;
Figure QLYQS_67
And->
Figure QLYQS_72
Are all acceleration factors; />
Step4, repeating Step2 and Step3 until the algorithm converges;
step5. Output algorithm updates the location information.
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